For nitrogen molecules, the average translational kinetic energy is what percent of the escape kinetic energy?
To find the average translational kinetic energy and escape kinetic energy of nitrogen molecules, we can use the formula for kinetic energy:
Kinetic Energy (KE) = (1/2) * m * v^2
where KE is the kinetic energy, m is the mass of the molecule, and v is the velocity.
First, let's find the average translational kinetic energy. The average is calculated by taking the average velocity, which is equal to the root-mean-square (RMS) velocity. The RMS velocity (v_rms) can be calculated using the formula:
v_rms = sqrt((3 * k * T) / m)
where k is the Boltzmann constant and T is the temperature in Kelvin.
Next, let's find the escape kinetic energy. The escape kinetic energy (KE_escape) is the minimum kinetic energy required for a molecule to escape the gravitational pull or confinement of a system. For a molecule to escape, its kinetic energy should be equal to or greater than the potential energy holding it in place.
Typically, the escape kinetic energy is given by the formula:
KE_escape = m * v_escape^2 / 2
where m is the mass of the molecule and v_escape is the escape velocity.
Now, let's find the percentage of the average translational kinetic energy compared to the escape kinetic energy:
Percent = (Average Translational KE / Escape KE) * 100
We need the value of m, which is the mass of a nitrogen molecule. The molar mass of nitrogen (N2) is approximately 28 grams/mol. So the mass of a single nitrogen molecule would be approximately 28 g/mol divided by Avogadro's number (6.022 x 10^23, which is the number of molecules in 1 mole).
Now that we have all the necessary formulas and constants, we can calculate the ratio and find the answer.